Reference no: EM133332165

Assignment: You own a grocery store chain that, among other things, sells bread to customers. You outsource the production of your bread to a bread manufacturing business (supplier) and want to assess the value of this specific product line to your company. Throughout this problem, assume that this product line will only operate for one period: in one year (i.e., at t = 1) and you can ignore taxes.

Your agreement with the supplier gives it flexibility in choosing the quantity of bread it delivers to you. Namely, the supplier chooses whether to deliver 50 or 75 million loaves of bread and it decides this at t = 1 on the basis of wheat prices at that time. However, if the supplier delivers 75 million loaves, it must pay your company a "supply increase fee" of $1.5m. Adjusting this delivery also costs the supplier $3.5m in "opportunity costs" (e.g., needing to reduce production of other goods to free up production capacity).

Additionally, the agreement with this supplier contains two clauses that govern the price per loaf that you pay to the supplier.

Price Grid (Clause 1): If wheat prices are less than $12.50 per bushel, the buyer will pay the supplier $1.20 per loaf. Otherwise, the buyer will pay the supplier $1.25 per loaf. Prices in this grid are subject to a minimum markup defined in Clause 2 of this contract.
Minimum Markup (Clause 2): The price per loaf paid by the buyer to the supplier is not to fall below a markup of 10% over the supplier's average production cost. Any "supply increase fee" and "opportunity costs" paid by the supplier when it increases its supply quantity should not be included when calculating the seller's average production cost. This clause takes precedence over the price grid defined in Clause 1 of this contract.
For example, Clause 2 implies that if the supplier's average production cost per loaf is $1.20, your company will pay $1.32 per loaf since the minimum price is 110% of $1.20 per loaf (which is higher than even the highest level in the price grid clause).

Finally, the public relations department of your company has made the following commitment to its customers:

• Price Commitment: During these uncertain and inflationary times, we commit to not raising prices for any of our goods unless our own costs for these goods exceed these prices. If this happens, we commit to only raising prices up to break-even levels.

You view this commitment as binding and define the break-even price of a product as the price level needed so that you earn a net cashflow of zero on that product line.

Currently, your company sells bread for $1.75 per loaf. In addition to paying your supplier for this bread, you have $0.40 in miscellaneous costs per loaf (e.g., storage costs). Assume that you can sell the entire supply of bread regardless of the quantity of bread delivered to you by the supplier. The supplier can produce 50 loaves of bread with a single bushel of wheat and it has a non-wheat cost of $0.80 per loaf. The current market price of wheat is $12.50 and assume the following: (i) the volatility of wheat prices is 35%, (ii) the convenience yield on wheat is 0%, and (iii) the riskless rate is 3%. All rates are expressed as continuously compounded annual rates.

Question: Determine the lowest minimum markup level that you would need to offer in a new agree- ment for the supplier to (rationally) accept the new proposal. In solving this problem, assume that the supplier interprets your proposal as a "take-it-or-leave-it" offer.